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thechocoluver445

  • 2 years ago

If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c. I know how to set this up and solve it, but for some reason I can't get the right answer.

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  1. thechocoluver445
    • 2 years ago
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    Here's what I did: |dw:1358034696496:dw| \[x = \sqrt{8^2 + 13^2 - 2(8)(13)(\cos 140°)}\]

  2. zepdrix
    • 2 years ago
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    Hmmm this is how I would do it :O So if we write our vectors in component form, we have,\[\large \vec{a}=8\cos100 \hat i+8\sin100 \hat j\]\[\large \vec c=13\cos60 \hat i+13\sin60 \hat j\]\[\large \vec a +\vec c=\color{#3366CF}{(8\cos100+13\cos60)\color{black}{\hat i}+(8\sin100+13\sin60)\color{black}{\hat j}}\] Hmm since 100 degrees isn't a nice special angle, we're going to get ugly decimal values it seems... So punch that into the calculator, then to get the MAGNITUDE of that vector we'll do uhhhh the thing, yah... I'm a little confused where your formula for x is coming from. It looks similar to the law of cosines. Maybe I just haven't done these types of problems in too long c: heh

  3. thechocoluver445
    • 2 years ago
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    Yeah I used law of cosines. If I add up all of the things in your method, I don't get the correct answer.

  4. zepdrix
    • 2 years ago
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    ah ok c: lemme take another shot at it. sec.

  5. zepdrix
    • 2 years ago
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    Hmm I'm not quite sure :c In your attempt at the problem, where is the 140 degree angle coming from?

  6. thechocoluver445
    • 2 years ago
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    180 - 40 = 140.

  7. thechocoluver445
    • 2 years ago
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    (In the parallelogram)

  8. mathmate
    • 2 years ago
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    Did you have a positive or negative value for cosine?

  9. mathmate
    • 2 years ago
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    What did you get for the magnitude?

  10. mathmate
    • 2 years ago
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    @thechocoluver445

  11. thechocoluver445
    • 2 years ago
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    It would be negative since the 140 is to the left of the y axis

  12. mathmate
    • 2 years ago
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    Sounds good. So your magnitude is greater than 13? What did you get? Is it a matter of number of decimals?

  13. mathmate
    • 2 years ago
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    @thechocoluver445 are you still there?

  14. thechocoluver445
    • 2 years ago
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    It's supposed to be 9.8 but I keep getting 19. something!

  15. thechocoluver445
    • 2 years ago
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    I'm pretty sure my way makes sense, but I don't know.

  16. thechocoluver445
    • 2 years ago
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    I just realized that my way was correct. Since the resultant is opposite an obtuse angle, it must be the longest side of the triangle. Thus, 9.8 cannot be the right answer! So I was correct. Thanks to everyone for helping. :)

  17. mathmate
    • 2 years ago
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    19.8 is correct for the problem you have posted..

  18. thechocoluver445
    • 2 years ago
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    The answer key was just wrong, lmao!

  19. thechocoluver445
    • 2 years ago
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    Yeah, that's what I got lol!

  20. thechocoluver445
    • 2 years ago
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    She probably just forgot the 1 before the 9.8 haha

  21. mathmate
    • 2 years ago
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    The only thing you may want to check to see if there are typos. It is possible that they modified the question but forgot to modify the key (which is half of the current answer).

  22. mathmate
    • 2 years ago
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    So go with 19.8.

  23. mathmate
    • 2 years ago
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    Oh, so it's not a printed key! That make it even more probably that the answer is wrong.

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